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Take a look at this picture (from APOD http://apod.nasa.gov/apod/ap110308.html): Saturn's rings at APOD

I presume that rocks within rings smash each other. Below the picture there is a note which says that Saturn's rings are about 1 km thick.
Is it an explained phenomenon?

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That's interesting. If I were asking about a puzzling question, after looking at the same picture or numbers, my question would be Why Saturn's rings are so thin? ;-) – Luboš Motl Mar 9 '11 at 8:01
@Luboš Motl - ;-) yes,yes. Thanks! – kakaz Mar 9 '11 at 8:16
Great to see this new harmony. ;-) By the way, some sources say that in some region, the thickness may be as small as 10 meters. Compare with the radius of Saturn which is 57,000,000 meters. The dynamics that created rings has to be about the angular momentum and collisions. Once the ring is thin enough, the rocks oscillate up-and-down away from the plane of the would-be ring, and collide, losing the up-down momentum along the way and getting more planar. However, I am not sure I can calculate - even approximately - the thickness expected now. – Luboš Motl Mar 9 '11 at 8:37
Even with initial velocities and bounded oscillations as shape of the rocks is irregular and collisions obviously not always central, there should be some drift away from the main plane of the rings. So I presume there should be some kind of mechanism which stabilise matter in such small volume. – kakaz Mar 9 '11 at 9:36
What makes a presumably more spherical protogalaxy to change to a disk? Same question for the formation of stars/planets out of a disk? BTW the rings are predominantly ice afaik. – Georg Mar 9 '11 at 12:01
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3 Answers

up vote 8 down vote accepted

There seems to be a known explanation. I quote from Composition, Structure, Dynamics, and Evolution of Saturn’s Rings, Larry W. Esposito (Annu. Rev. Earth Planet. Sci. 2010.38:383-410):

[The] rapid collision rate explains why each ring is a nearly flat disk. Starting with a set of particle orbits on eccentric and mutually inclined orbits (e.g., the fragments of a small, shattered moon), collisions between particles dissipate energy but also must conserve the overall angular momentum of the ensemble. Thus, the relative velocity is damped out, and the disk flattens after only a few collisions to a set of nearly coplanar, circular orbits.

I think the key is that particles in a thick ring would not move in parallel planes but would have slanted trajectories, colliding all the time and losing their energy very fast.

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So essential point, in my opinion is, that it is a matter of initial conditions. Picture You are pointing out begins with "fragments of small shattered moon" and it is the same for comment of anna v above. I would like to wait if a few answers appear here, but I am ready to accept Your answer here. – kakaz Mar 9 '11 at 14:34
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In inelastic collisions between the ring particles angular momentum is preserved but kinetic energy is lost. So the final rotation axis of the rings is given by their initial angular momentum but it is the dynamical evolution of the rings that makes them flat and thin. – Alejandro Luque Mar 9 '11 at 14:54
I would add that the tides should also be taken into account: the gradual increase of angular momentum of the rings due to the tides the rings induce on Saturn. It is not only collisions, because the orbits will expand differentially, depending on the mass of the debris, contributing to thinning. – anna v Mar 10 '11 at 5:56
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I know exactly why the rings are so flat. The answer is so simple you will smack your head. The first clue is, what is the shape of the gas giant? It is far from circular. It is far wider at its equator. Centripetal force causes a thicker equator. Therefore because the thickness is far wider at the equator, the gravitation at the equator is more than that at the poles.Therefore the particles of the rings fall into the greatest gravity well.

It is like holding a ball on a string. All around you there is vast amounts of matter pulling from your right and left. But the central point of the earth is the focal of the most amount of matter pulling it straight down. On the gas giants, it is at the equator.

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Some numbers to support this argument would be useful. – Alec S Apr 9 at 17:50
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If one could assume that the ring is a continuous distribution of mass, we could try minimizing the total energy of the system (self energy + energy of interaction with Saturn). These two conditions along with the condition that total mass of the disc is a constant, would (I think) leave us with a unique geometry (inner and outer radius, thickness).

EDIT: Some Googling gave this paper: http://dx.doi.org/10.1016/0019-1035(79)90084-8

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It is clever idea but too simple and vague. I would like to know why internal structure of the rings, namely scattering do not destroy its thickness, and continuous model is probably wrong here. Note also here that it is not clear if energy is the only possible bonds here: there is angular momentum, possible entropy, maybe perturbations from other Saturn moons etc. For example consider Earth and its artificial satellites - they do not form "rings" in natural way, so probably idea that mineralisation of energy is enough is too simple - You have at least prober initial conditions. – kakaz Mar 9 '11 at 14:39
@kakaz I agree, but how would you know which parameter is to be given more importance? – Manu Mar 9 '11 at 14:56
@mnnttl - by numerical experiments for example. You cannot explain something by just assuming other things. There should be an evidence for certain assumption - energy is usually very general notion, and so it works, but also is usually not enough alone to provide correct model - see thermodynamics for example. – kakaz Mar 9 '11 at 20:32

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